WASHINGTON — Nearly 10 years after a U.S.-led coalition attacked Afghanistan and 18 months after a surge of 33,000 fresh American troops there, war-weary U.S. voters probably will cheer President Barack Obama's speech Wednesday night announcing his timetable to start withdrawing troops from America's longest war.

But whether the drawdown helps or hurts Afghanistan — and ultimately what Americans think of how Obama handled it as he heads into his 2012 re-election contest — will depend on how fast troops come home and how quickly Afghans can step in to replace them.

"He has been working through his decision over the course of the last several weeks and finalized that decision today," White House spokesman Jay Carney said Tuesday.

The president will explain his timetable for withdrawal in a televised speech from the White House at 8 p.m. EDT. He'll travel Thursday to talk firsthand with troops at Fort Drum, N.Y., the home of the Army's 10th Mountain Division.

Obama, who decided in December 2009 to send an additional 33,000 troops to Afghanistan for a total of 100,000, said at the time that he'd start drawing down the surge in July 2011, and later that he'd pull all U.S. combat troops out by the end of 2014.

He's expected to announce Wednesday night the drawdown of 5,000 troops starting next month, and the full 33,000 by the end of next year. The remaining 67,000 troops would be drawn down over the following two years.

"The parameters of the decision involve the beginning of the drawdown of U.S. forces," Carney said Tuesday. "This is within a framework of the gradual transition of security lead to the Afghans. It's begun already in some places, but it will progress over the next several years."

At least 1,631 U.S. troops have been killed as part of the Afghanistan campaign since 2001, according to icasualties.org, which tracks casualties in the wars in Afghanistan and Iraq.

Obama's under growing political pressure to draw down the troops quickly, particularly since U.S. Navy SEALs killed terrorist mastermind Osama bin Laden on May 2 in Pakistan. Bin Laden's terrorist network and the Taliban regime that harbored it were the prime targets of the invasion of Afghanistan in 2001.

The number of Americans who want to withdraw troops as soon as possible jumped after the killing of bin Laden and is at an all-time high, the nonpartisan Pew Research Center reported Tuesday.

For the first time, a majority, 56 percent, want the troops brought home as soon as possible, while just 39 percent support keeping the troops there until the country is stabilized.

In Congress, Senate Armed Services Committee Chairman Carl Levin, D-Mich, argued Tuesday that a major troop reduction would accelerate Afghanistan's own hand in its security.

"A significant reduction in our troop level this year would send a critical signal to Afghan leaders that we mean it when we say our commitment is not open-ended and that they need to be urgently focused on preparing Afghan security forces to assume security responsibility for all of Afghanistan," said Levin, who wants at least 15,000 U.S. soldiers withdrawn this year.

Outgoing Secretary of Defense Robert Gates noted the pressure on Obama.

"The president has to take into account on any national security issue sustainability here at home, both among the public and in the Congress," Gates said at a news conference Tuesday. "And it goes without saying that there are a lot of reservations in the Congress about the war in Afghanistan."

Gates, however, is also among several senior U.S. officials who are concerned that a drawdown that's too rapid and extensive could allow the Taliban to recapture areas of their southern heartland that the U.S. surge pushed them out of.

Ali Jalali, Afghanistan's first post-Taliban interior minister, said Afghan forces "are not ready" to assume security in those parts of Kandahar and Helmand provinces.

Moreover, he said that the drawdown would reduce the chances that leaders of the Taliban and other insurgent groups would accept calls by the U.S., its allies and Afghan President Hamid Karzai to begin negotiating a political settlement of the war.

Pulling out U.S. forces too quickly — such as pledging to withdraw the 33,000 surge troops by the end of next year — could destabilize the country, said Robert Lamb, a senior fellow at the Center for Strategic and International Studies, a Washington research center.

"We do need to start withdrawing," he said. "My concern is that we do it at a rate that is constructive."

Withdrawing too quickly, he said, could throw Afghanistan's dependent economy into a depression and create an opening for new anti-American sentiment. It also would risk creating "a political vacuum that could be filled by any number of actors."